1. Field of the Invention
The field of the invention relates to gemstones and jewelry, and more particularly to enhancing the optical characteristics of a gemstone and jewelry.
2. Description of the Related Art
Gemstones are prized for their rarity and beauty. Among gemstones, diamonds, in particular, are highly valued. Apart from their worth in industrial applications, diamonds are considered symbols of love, beauty, and purity in many cultures. When used for their aesthetic quality, diamond crystals are often cut and polished in ways that emphasize certain optical properties such as their brilliance or fire. This is especially true of the round brilliant cut, whose optical properties were studied and mathematically characterized in a paper by Marcel Tolkowsky in 1919.
FIG. 1 illustrates a typical round brilliant cut diamond 100. The round brilliant cut includes an upper crown portion 130. The crown 130 generally has a flat top portion, known as the table 110. The lower portion of the round brilliant cut is the pavilion 150, whose tip is called the culet 160. Very often the crown 130 and the pavilion 150 are separated by a flat girdle 140 of some width to help prevent chipping that might otherwise occur if the crown 130 and pavilion 150 were joined at a sharp angle. The diameter of the round brilliant cut at the girdle 140 is called the spread of the diamond. The round brilliant cut also has a number of generally flat facets 170.
Tolkowsky began his study of the round brilliant cut with a poll of passersby on city streets to determine the crown 130 and pavilion 150 angles and heights, as well as their proportions to the spread 120 and table 110 width, which people found to be the most beautiful. Tolkowsky then undertook a study of the round brilliant cut and showed mathematically that the diamonds which the public found to be most beautiful were those whose angles and proportions resulted in a better balance of brilliance and fire than round brilliant cuts of other dimensions.
The brilliance of the cut refers, in part, to its brightness in terms of the amount of light that it reflects to a face-up observer (viewing the diamond crown 130 perpendicularly to the table 110 surface). Due to the geometry of the round brilliant cut, much of the light that enters the crystal from above is reflected by the walls of the pavilion 150, the pavilion, in effect, acting as a corner reflector, and returned toward an observer through the crown 130. Light that is not reflected back towards the observer is said to have “leaked” out of the diamond.
Fire, in contrast, refers to the rainbow of colors produced by the diamond, noticeable mainly at the crown facets 170. This effect is due to the relatively high dispersion or wavelength dependence of the refractive index of diamond. Dispersion causes light of different wavelengths to be refracted different amounts upon entering the facets of the diamond. These different wavelengths then propagate along separate optical paths through the diamond and also exit the stone at distinct angles as well. Flashes of color may thus be seen at different angles of view. This effect is enhanced as light exits the diamond near the critical angle between the diamond-to-air interface. This strong ability to split white light into its component colors is an important aspect of diamond's attraction as a gemstone, giving it impressive prismatic action that results in the fire of a well-cut stone.
While Tolkowsky calculated “ideal” angles and proportions for a round brilliant cut diamond that gave “the most vivid fire and the greatest brilliancy,” he also noted, of the pavilion angle in particular, that although “a greater angle would give better reflection, this would not compensate for the loss due to the corresponding reduction in dispersion.” Thus, a round brilliant cut diamond, as well as any other style of cut, faces tradeoffs between brilliance and fire, with the most beautiful cuts achieving a delicate balance between the two. For example, steep crown angles and small tables tend to increase fire (a larger table size means a smaller crown facet area—the part that creates the most dispersion) in a round brilliant cut diamond but also decrease the amount of brilliance. To make matters worse, a diamond cutter must consider many other factors when cutting a particular diamond crystal, which may result in a gem of less beauty than might be possible if the diamond were cut exclusively with its optical properties in mind. These factors include the desire to remove as little material as possible from the rough diamond crystal during the cutting process; the desire to exclude inclusions from the final cut; the desire to target certain carat weights which are typically more sought after by consumers (i.e. ½, 1, 2, carat, etc.); and the desire to use certain high-seller fancy cuts such as princess, marquise, pear, oval, heart, etc. These competing factors generally do not allow a diamond crystal to be cut in such a way as to simultaneously maximize brilliance and fire, or in many instances, to even achieve the “ideal” balance between the two.